To me, none of these looks like a case for using the Abel/Dirichlet tests. I would use the (limit) comparison test for all of them.
Taking as an example, start by looking at the function If we can approximate this by a power of x, as , then by putting we can estimate the size of
Using the first couple of terms in the power series , you get the approximation Now use a power series approximation again, putting in the series for , to get
You will notice that that is a very casual, nonrigorous argument. But now that we have discovered that , we can look at the ratio and prove rigorously (by repeated applications of l'H˘pital's rule, for example), that
Finally, you can put and deduce that , where and Since converges, it follows from the limit comparison test that converges absolutely.